The financial media is partly to blame for the huge movement out of bonds, according to Douglas Hodge, chief operating officer of bond giant Pimco, who said that net inflows to bonds will return over the longer term.
"In the aftermath of the financial crisis,the media—which play a large role in setting the tone of the markets and the psyche of investors—went from being cheerleaders for bonds, stressing their virtues and role in maintaining a diversified portfolio, to romancing the notion that bonds are riskier than stocks," Hodge said in an piece posted on the California-based firm's website on Monday.
"While the media may have succeeded in sullying sentiment, their message that bonds are riskier than stocks is untenable," he added.
(Read more: Treasury to reach debt limit by mid-October)
Concerns about an imminent tapering off of Federal Reserve asset purchases have led a flight to cash from equity and bond funds. Bond yields have been on a one-way ticket higher since May, when the Fed's policy minutes sparked fears it would start scaling back quantitative easing this year.
Outflows from U.S. bond mutual funds and exchange traded funds accelerated in August, according to TrimTabs, following record outflows of $69.1 billion in June, and outflows of $14.8 billion in July.
"These outflows mark an enormous shift for the bond world. This summer's redemptions broke a string of 21 consecutive monthly inflows," TrimTabs CEO David Santschi said in the note Sunday. "Moreover, bond funds have redeemed $10.3 billion year-to-date, putting them on track to post their lowest annual flow since at least 2004."
The yield on 10-year benchmark Treasurys spiked above 2.93 percent last week, a high not seen since July 2011. This week, rates have steadied, with the yield falling to 2.711 percent on Tuesday.
Many believe yields will burst through the crucial 3 percent level with the release of U.S. nonfarm payrolls data on Sept. 6. However, Hodge said, if rates continue to rise in the short-term, they would likely do so gradually, rather than with a sudden spike.
(Read more: Bond exodus accelerates as yields creep nearer 3%)
"Individuals may have been rushing to the exits, but many of America's largest corporate pension funds and insurance companies have been buying long-dated bonds. The long maturities may help to de-risk their portfolios over the long-term. ... We expect individual investors will eventually follow suit, once more becoming net investors in fixed income," Hodge said.
He argued that bonds are more stable than stocks and that the latter will suffer if rates continue to rise over a sustained period.
Active bond fund managers can sift through a wide range of bond sectors, and deploy various strategies to find value, even while rates are rising, Hodge said. He added that demand for fixed income will grow because of the rapidly increasing pool of retirees in developed countries and growing numbers of wealthy people in emerging economies.
"Though it is easy to get caught up in the fear and greed that can propel markets to extremes and create unwelcome volatility, investors should not lose sight of their financial goals, or the basic precepts of investing. The journey to financial security is a long one. It is full of bumps and turns ... and the occasional inflection point," Hodge said.
By CNBC.com's Matt Clinch. Follow him on Twitter @mattclinch81